Diverging Parallels
Author: Arie Nicolaas Jan Den Hollander
Publisher: Brill Archive
Published: 1971
Total Pages: 238
ISBN-13:
DOWNLOAD EBOOK →Author: Arie Nicolaas Jan Den Hollander
Publisher: Brill Archive
Published: 1971
Total Pages: 238
ISBN-13:
DOWNLOAD EBOOK →Author: James F. T. Bugental
Publisher: W. W. Norton & Company
Published: 1992-09
Total Pages: 344
ISBN-13: 9780393309119
DOWNLOAD EBOOK →Unlike the brief, specific-solution oriented therapies that many people demand today, the goal of depth therapy is life change. James Bugental has been practicing, teaching and writing about depth therapy for 40 years, and in this book, he shares his experiences as a psychotherapist.
Author: Granville Stanley Hall
Publisher:
Published: 1918
Total Pages: 500
ISBN-13:
DOWNLOAD EBOOK →Author: Henry William Ellsworth
Publisher:
Published: 1862
Total Pages: 262
ISBN-13:
DOWNLOAD EBOOK →Author: Robert G. Bill
Publisher: Xlibris Corporation
Published: 2023-03-19
Total Pages: 267
ISBN-13: 1669853047
DOWNLOAD EBOOK →The story of the development of geometry is told as it emerged from the concepts of the ancient Greeks, familiar from high school, to the four-dimensional space-time that is central to our modern vision of the universe. The reader is first reacquainted with the geometric system compiled by Euclid with its postulates thought to be self-evident truths. A particular focus is on Euclid’s fifth postulate, the Parallel Postulate and the many efforts to improve Euclid’s system over hundreds of years by proving it from the first four postulates. Two thousand years after Euclid, in the process that would reveal the Parallel Postulate as an independent postulate, a new geometry was discovered that changed the understanding of geometry and mathematics, while paving the way for Einstein’s General Relativity. The mathematics to describe the non-Euclidean geometries and the geometric universe of General Relativity is initiated in the language of mathematics available to a general audience. The story is told as a mathematical narrative, bringing the reader along step by step with all the background needed in analytic geometry, the calculus, vectors, and Newton’s laws to allow the reader to move forward to the revolutionary extension of geometry by Riemann that would supply Einstein with the language needed to overthrow Newton’s universe. Using the mathematics acquired for Riemannian geometry, the principles behind Einstein’s General Relativity are described and their realization in the Field Equations is presented. From the Field Equations, it is shown how they govern the curved paths of light and that of planets along the geodesics formed from the geometry of space-time, and how they provide a picture of the universe’s birth, expansion, and future. Thus, Euclid’s geometry while no longer thought to spring from perceived absolute truths as the ancients believed, ultimately provided the seed for a new understanding of geometry that in its infinite variety became central to the description of the universe, marking mathematics as a one of the great modes of human expression.
Author: Lakhmir Singh & Manjit Kaur
Publisher: S. Chand Publishing
Published:
Total Pages:
ISBN-13: 935501029X
DOWNLOAD EBOOK →A series of six books for Classes IX and X according to the CBSE syllabus. Each class divided into 3 parts. Part 1 - Physics Part 2 - Chemistry Part 3 - Biology